Turn on the night vision goggles and look down the tunnel to the right. Engage the group of soldiers and keep firing. They should be fairly confused, so it's not hard to take them out quickly. Go to the end of the hallway for another meeting with some friendly fire. Then pop off the goggles and clear the tunnel. There are just a few men, so it shouldn't be any problem.

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Go further down and into the catwalk by the pipes. Kill the few guards left on the catwalk, but don't chase the ones at the end. They should step out into the next area and set up an ambush for you. As soon as the wall on the right side of the catwalk ends, turn to the right and quickly take out the 3 guys waiting for you.
Advance and regroup for another breach. There's several guys in the shower area. Just take out whoever you can and move into the room. I found the riot shield to be surprisingly effective right here. Regardless, if you haven't swapped it out by now, you should. Try to get a shotgun.
Some heavy assault troops will move into the shower room as you advance. The only way to counter them is to give them a good blast from the side with a shotgun. Their riot shield won't protect them against being outflanked. The shotgun also has a good chance of nicking them on an unprotected spot and getting them to drop their guard.
The most important thing to remember is that you can fall back to the first room. Use grenades to clear the guards off of the balcony and use the shotgun to wear away at the assault troops. Once the room is finally clear, advance with Soap. Just sprint forward and drop down the hole into the tunnel system. Follow Soap down the tunnel until you end up at the breach point. Don't bother trying to take out the soldier. Prisoner 627 has it all taken care of. It's good to see our old friend.
Run on out to try and reach the helicopter. You won't be able to outrun the collapse though. Follow them down the other path into the central room. You'll be hit in the head with debris, but that's basically just the signal. Once you come to, just hook into the SPIE line and ride it out of the gulag.